Supervised Learning in image enhance from electron microscopy inversion results

In Nondestructive testing there is a variety of applications in Material Science, where the specimen is imaged by an Electron Microscope and then by image inversion, informationis extracted for the material interior. This type of information might contain noise either by the imaging procedure or by the numerical part of the inversion. We present a method that can improve the interior density results of an inversed material from a series of Scanning Electron Microscope (SEM) images. For this method, the material density can contain some discontinuity, such as regions where it is dense and regions where there are voids.The proposed method directly stands on the Bayesian learning framework, adopting Gaussian Stochastic Processes (GSPs). Two test sample cases that contain some discontinuities in the density are tested. We also provide a comparison between two different GSP modelling approaches; one is a typical GSP and the other accounts for discontinuity, by introducing hyperparameters. The GSP method gives reconstructed data in reasonable agreement with the known original density distribution, giving confidence that the method can be applied to experimentally obtained SEM images.

Quantification of Fracture Roughness by Change Probabilities and Hurst Exponents

The objective of the current study is to utilize an innovative method called “change probabilities” for describing fracture roughness. In order to detect and visualize anisotropy of rock joint surfaces, the roughness of one-dimensional profiles taken in different directions is quantified. The central quantifiers, change probabilities, are based on counting monotonic changes in discretizations of a profile. These probabilities, which usually vary with the scale, can be reinterpreted as scale-dependent Hurst exponents. For a large class of Gaussian stochastic processes, change probabilities are shown to be directly related to the classical Hurst exponent, which generalizes a relationship known for fractional Brownian motion. While related to this classical roughness measure, the proposed method is more generally applicable, therefore increasing the flexibility of modeling and investigating surface profiles. In particular, it allows a quick and efficient visualization and detection of roughness anisotropy and scale dependence of roughness.

Probabilistic analysis of random nonlinear oscillators subject to small perturbations via probability density functions: theory and computing

We study a class of single-degree-of-freedom oscillators whose restoring function is affected by small nonlinearities and excited by stationary Gaussian stochastic processes. We obtain, via the stochastic perturbation technique, approximations of the main statistics of the steady state, which is a random variable, including the first moments, and the correlation and power spectral functions. Additionally, we combine this key information with the principle of maximum entropy to construct approximations of the probability density function of the steady state. We include two numerical examples where the advantages and limitations of the stochastic perturbation method are discussed with regard to certain general properties that must be preserved.